What is the expected value of Δ T f for 1.25 m CaCl 2 solution if 1.25 m sucrose solution has Δ T f value x K ?

Question

What is the expected value of Δ T f ​ for 1.25 m CaCl 2 ​ solution if 1.25 m sucrose solution has Δ T f ​ value x K ?

TestHub · Accepted Answer

The depression in freezing point is given by the formula:

$Δ T_{f} = i \times K_{f} \times m$

For sucrose, which is a non-electrolyte, the van't Hoff factor $i = 1$ .

$Δ T_{f} (sucrose) = 1 \times K_{f} \times 1.25 = x$

For $CaCl_{2}$ , it is a strong electrolyte and dissociates into three ions (one $Ca^{2 +}$ and two $Cl^{-}$ ), so the van't Hoff factor $i = 3$ .

$Δ T_{f} (CaCl_{2}) = 3 \times K_{f} \times 1.25$

Substituting the value of $K_{f} \times 1.25$ from the sucrose equation:

$Δ T_{f} (CaCl_{2}) = 3 \times x = 3 x K$

Answer: $3 x$ K

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